A salon and a cafe, 500 m apart, are situated between Hilda's house and Cindy's house. The cafe is halfway between the two houses and the salon is closer to Cindy's house. Hilda and Cindy left their homes at the same time and arrived at the salon at the same time. Hilda drove at a speed of 61 km/h while Cindy drove at a speed 20 km/h slower than Hilda. Leaving your answer in kilometres,

1. how much farther did Hilda travel than Cindy?
2. how far is Cindy's house from the cafe?

(a)
Let the distance between Hilda's house and Cindy's house be 1 d.
Cindy travelled = ¹₂ d - 500 m
Hilda travelled = ¹₂ d + 500 m

Distance that Hilda travelled more than Cindy
= ¹₂ d + 500 - (¹₂ d - 500)
= ¹₂ d + 500 - ¹₂ d + 500
= 1000 m
= 1 km

(b)
Time that Hilda took to travel to the salon
= 1 ÷ 20
= ¹₂₀ h

Distance that Hilda travelled
= ¹₂₀ x 61
= 3.05 km

1000 m = 1 km
500 m = 0.5 km

Distance between Cindy's house and the cafe
= 3.05 - 0.5
= 2.55 km

Answer(s): (a) 1 km; (b) 2.55 km